How to allow Rigid Body Physics take over after follow path constraint?
At the frame before you want to switch from the "follow path" to rigid body, keyframe the "Follow Path" Constraint influence to "1" by hovering over the influence slider and pressing "i". Then go ahead one frame and set the influence to "0" and keyframe the influence again.

Then to do the same thing on the same frames to your rigid body. (I believe the dynamic checkbox controls the rigid body the same way the influence slider would for the "follow Path", but I'm not 100% sure.)